Time zones and daylight saving time are a complicated business. The conversions to and from Julian and Unix-style dates automatically compute the correct time zone and daylight saving adjustment to use, provided they can figure out this information. This section describes Calc's time zone adjustment algorithm in detail, in case you want to do conversions in different time zones or in case Calc's algorithms can't determine the right correction to use.
Adjustments for time zones and daylight saving time are done by t U, t J, t N, and t C, but not by any other commands. In particular, ‘<may 1 1991> - <apr 1 1991>’ evaluates to exactly 30 days even though there is a daylight-saving transition in between. This is also true for Julian pure dates: ‘julian(<may 1 1991>) - julian(<apr 1 1991>)’. But Julian and Unix date/times will adjust for daylight saving time: using Calc's default daylight saving time rule (see the explanation below), ‘julian(<12am may 1 1991>) - julian(<12am apr 1 1991>)’ evaluates to ‘29.95833’ (that's 29 days and 23 hours) because one hour was lost when daylight saving commenced on April 7, 1991.
In brief, the idiom ‘julian(date1) - julian(date2)’ computes the actual number of 24-hour periods between two dates, whereas ‘date1 - date2’ computes the number of calendar days between two dates without taking daylight saving into account.
tzone] command converts the time
zone specified by its numeric prefix argument into a number of
seconds difference from Greenwich mean time (GMT). If the argument
is a number, the result is simply that value multiplied by 3600.
Typical arguments for North America are 5 (Eastern) or 8 (Pacific). If
Daylight Saving time is in effect, one hour should be subtracted from
the normal difference.
If you give a prefix of plain C-u,
calc-time-zone (like other
date arithmetic commands that include a time zone argument) takes the
zone argument from the top of the stack. (In the case of t J
and t U, the normal argument is then taken from the second-to-top
stack position.) This allows you to give a non-integer time zone
adjustment. The time-zone argument can also be an HMS form, or
it can be a variable which is a time zone name in upper- or lower-case.
For example ‘tzone(PST) = tzone(8)’ and ‘tzone(pdt) = tzone(7)’
(for Pacific standard and daylight saving times, respectively).
North American and European time zone names are defined as follows; note that for each time zone there is one name for standard time, another for daylight saving time, and a third for “generalized” time in which the daylight saving adjustment is computed from context.
YST PST MST CST EST AST NST GMT WET MET MEZ 9 8 7 6 5 4 3.5 0 -1 -2 -2 YDT PDT MDT CDT EDT ADT NDT BST WETDST METDST MESZ 8 7 6 5 4 3 2.5 -1 -2 -3 -3 YGT PGT MGT CGT EGT AGT NGT BGT WEGT MEGT MEGZ 9/8 8/7 7/6 6/5 5/4 4/3 3.5/2.5 0/-1 -1/-2 -2/-3 -2/-3
To define time zone names that do not appear in the above table,
you must modify the Lisp variable
is a list of lists describing the different time zone names; its
structure is best explained by an example. The three entries for
Pacific Time look like this:
( ( "PST" 8 0 ) ; Name as an upper-case string, then standard ( "PDT" 8 -1 ) ; adjustment, then daylight saving adjustment. ( "PGT" 8 "PST" "PDT" ) ) ; Generalized time zone.
With no arguments,
calc-time-zone or ‘tzone()’ will by
default get the time zone and daylight saving information from the
calendar (see Calendar/Diary). To use a different time zone, or if the
calendar does not give the desired result, you can set the Calc variable
TimeZone (which is by default
nil) to an appropriate
time zone name. (The easiest way to do this is to edit the
TimeZone variable using Calc's s T command, then use the
s p (
calc-permanent-variable) command to save the value of
If the time zone given by
TimeZone is a generalized time zone,
EGT, Calc examines the date being converted to tell whether
to use standard or daylight saving time. But if the current time zone
is explicit, e.g.,
EDT, then that adjustment is
used exactly and Calc's daylight saving algorithm is not consulted.
The special time zone name
is equivalent to no argument; i.e., it uses the information obtained
from the calendar.
The t J and
t U commands with no numeric prefix
arguments do the same thing as ‘tzone()’; namely, use the
information from the calendar if
otherwise use the time zone given by
When Calc computes the daylight saving information itself (i.e., when
TimeZone variable is set), it will by default consider
daylight saving time to begin at 2 a.m. on the second Sunday of March
(for years from 2007 on) or on the last Sunday in April (for years
before 2007), and to end at 2 a.m. on the first Sunday of
November. (for years from 2007 on) or the last Sunday in October (for
years before 2007). These are the rules that have been in effect in
much of North America since 1966 and take into account the rule change
that began in 2007. If you are in a country that uses different rules
for computing daylight saving time, you have two choices: Write your own
daylight saving hook, or control time zones explicitly by setting the
TimeZone variable and/or always giving a time-zone argument for
the conversion functions.
The Lisp variable
math-daylight-savings-hook holds the
name of a function that is used to compute the daylight saving
adjustment for a given date. The default is
math-std-daylight-savings, which computes an adjustment
(either 0 or -1) using the North American rules given above.
The daylight saving hook function is called with four arguments:
The date, as a floating-point number in standard Calc format;
a six-element list of the date decomposed into year, month, day,
hour, minute, and second, respectively; a string which contains
the generalized time zone name in upper-case, e.g.,
and a special adjustment to be applied to the hour value when
converting into a generalized time zone (see below).
The Lisp function
math-prev-weekday-in-month is useful for
daylight saving computations. This is an internal version of
pwday function described in the previous
section. It takes four arguments: The floating-point date value,
the corresponding six-element date list, the day-of-month number,
and the weekday number (0–6).
The default daylight saving hook ignores the time zone name, but a more sophisticated hook could use different algorithms for different time zones. It would also be possible to use different algorithms depending on the year number, but the default hook always uses the algorithm for 1987 and later. Here is a listing of the default daylight saving hook:
(defun math-std-daylight-savings (date dt zone bump) (cond ((< (nth 1 dt) 4) 0) ((= (nth 1 dt) 4) (let ((sunday (math-prev-weekday-in-month date dt 7 0))) (cond ((< (nth 2 dt) sunday) 0) ((= (nth 2 dt) sunday) (if (>= (nth 3 dt) (+ 3 bump)) -1 0)) (t -1)))) ((< (nth 1 dt) 10) -1) ((= (nth 1 dt) 10) (let ((sunday (math-prev-weekday-in-month date dt 31 0))) (cond ((< (nth 2 dt) sunday) -1) ((= (nth 2 dt) sunday) (if (>= (nth 3 dt) (+ 2 bump)) 0 -1)) (t 0)))) (t 0)) )
bump parameter is equal to zero when Calc is converting
from a date form in a generalized time zone into a GMT date value.
It is -1 when Calc is converting in the other direction. The
adjustments shown above ensure that the conversion behaves correctly
and reasonably around the 2 a.m. transition in each direction.
There is a “missing” hour between 2 a.m. and 3 a.m. at the beginning of daylight saving time; converting a date/time form that falls in this hour results in a time value for the following hour, from 3 a.m. to 4 a.m. At the end of daylight saving time, the hour from 1 a.m. to 2 a.m. repeats itself; converting a date/time form that falls in this hour results in a time value for the first manifestation of that time (not the one that occurs one hour later).
nil, then the
daylight saving adjustment is always taken to be zero.
In algebraic formulas, ‘tzone(zone, date)’ computes the time zone adjustment for a given zone name at a given date. The date is ignored unless zone is a generalized time zone. If date is a date form, the daylight saving computation is applied to it as it appears. If date is a numeric date value, it is adjusted for the daylight-saving version of zone before being given to the daylight saving hook. This odd-sounding rule ensures that the daylight-saving computation is always done in local time, not in the GMT time that a numeric date is typically represented in.
The ‘dsadj(date, zone)’ function computes the
daylight saving adjustment that is appropriate for date in
time zone zone. If zone is explicitly in or not in
daylight saving time (e.g.,
date is ignored. If zone is a generalized time zone,
the algorithms described above are used. If zone is omitted,
the computation is done for the current time zone.